Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
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arXiv
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| Autores principales: | , , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911207513915392 |
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| author | Soares, Rafael D. Gal, Youenn Le Leung, Chun Y. Meidan, Dganit Romito, Alessandro Schirò, Marco |
| author_facet | Soares, Rafael D. Gal, Youenn Le Leung, Chun Y. Meidan, Dganit Romito, Alessandro Schirò, Marco |
| contents | Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by the competition between unitary dynamics and dissipation. In this work, we reveal the fundamental role of conservation laws in shaping this competition. Focusing on translation-invariant non-interacting fermionic models with U(1) symmetry, we present a theoretical framework to understand the structure of the steady-state of these models and their entanglement content based on two ingredients: the nature of the spectrum of the non-Hermitian Hamiltonian and the constraints imposed on the steady-state single-particle occupation by the conserved quantities. These emerge from an interplay between Hamiltonian symmetries and initial state, due to the non-linearity of measurement back-action. For models with complex energy spectrum, we show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue. As a result, one can have partially filled or fully filled bands in the steady-state, leading to an entanglement entropy undergoing a filling-driven transition between critical sub volume scaling and area-law, similar to ground-state problems. Conversely, when the spectrum is fully real, we provide evidence that local observables can be captured using a diagonal ensemble, and the entanglement entropy exhibits a volume-law scaling independently on the initial state, akin to unitary dynamics. We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model, uncovering a rich interplay between the single-particle spectrum and conservation laws in determining the steady-state structure and the entanglement transitions. These conclusions are supported by exact analytical calculations and numerical calculations relying on the Faber polynomial method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_08557 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices Soares, Rafael D. Gal, Youenn Le Leung, Chun Y. Meidan, Dganit Romito, Alessandro Schirò, Marco Statistical Mechanics Quantum Physics Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by the competition between unitary dynamics and dissipation. In this work, we reveal the fundamental role of conservation laws in shaping this competition. Focusing on translation-invariant non-interacting fermionic models with U(1) symmetry, we present a theoretical framework to understand the structure of the steady-state of these models and their entanglement content based on two ingredients: the nature of the spectrum of the non-Hermitian Hamiltonian and the constraints imposed on the steady-state single-particle occupation by the conserved quantities. These emerge from an interplay between Hamiltonian symmetries and initial state, due to the non-linearity of measurement back-action. For models with complex energy spectrum, we show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue. As a result, one can have partially filled or fully filled bands in the steady-state, leading to an entanglement entropy undergoing a filling-driven transition between critical sub volume scaling and area-law, similar to ground-state problems. Conversely, when the spectrum is fully real, we provide evidence that local observables can be captured using a diagonal ensemble, and the entanglement entropy exhibits a volume-law scaling independently on the initial state, akin to unitary dynamics. We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model, uncovering a rich interplay between the single-particle spectrum and conservation laws in determining the steady-state structure and the entanglement transitions. These conclusions are supported by exact analytical calculations and numerical calculations relying on the Faber polynomial method. |
| title | Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2504.08557 |